ninetyone

Ninety-one, written as 91 in decimal, is the natural number that follows ninety and precedes ninety-two. It is an odd composite number, with prime factorization 7 × 13, making it a semiprime (a product of two primes).

In mathematics, 91 has several notable representations and properties. It is a triangular number, specifically the 13th triangular number, since T13 = 13 × 14 / 2 = 91. It is also a centered hexagonal number, given by the formula 3n(n−1) + 1, with n = 6 yielding 91. In Roman numerals, it is written as XCI.

Representations of 91 in different bases include binary 1011011, octal 133, and hexadecimal 5B. In decimal, 91 is congruent to 0 modulo 7 and modulo 13, reflecting its status as the product of these two primes.

Beyond pure mathematics, 91 has appeared as a calendar year in history, and as a numeric label in various contexts. It is related to nearby numbers such as 90 and 92 through simple arithmetic, and to broader families of numbers including triangular numbers, semiprimes, and centered hexagonal numbers.

See also: 90 (ninety), 92 (ninety-two), triangular numbers, semiprimes, centered hexagonal numbers.